Mr. Thomas' Salary

Date: 9/6/96 at 7:0:32
From: Anonymous
Subject: Mr. Thomas' Salary
Mr. Thomas received his salary and immediately spent 1/12 of it to buy
himself a watch and 3/11 of the remaining to pay for a new television
set for the family. He then gave his wife $550 for her expenses and
deposited the rest of the money, which amounted to $1050 into the
bank. How much was his salary?

Hi!
Let S = Mr. Thomas's salary.
Mr. Thomas spent 1/12 of S on a new watch.
Subtracting the 1/12 of S he spent from the amount he started
with (12/12 of S) leaves:
12/12 - 1/12 = 11/12 of S remaining.
Then he spent 3/11 of that remaining 11/12 on a TV.
Again, subtract the amount he spent ( 3/11 of 11/12 of S which =
3/11 * 11/12 = 3/12 of S) from the total he had before (11/12 of S).
This leaves 11/12 - 3/12 = 8/12 of S.
He then gave $550 to his wife and put $1050 in the bank. This
accounted for the remainder of the money. This means that 550 + 1050
is the amount he had left after buying the TV and the watch which we
found to be 8/12 of S.
So 550 + 1050 = 1600 = 8/12 of S.
Writing in a standard equation form:
1600 = 8/12 * S
Now solve for S
12 * 1600 / 8 = S
S = 2400.
So Mr. Thomas' salary was $2400.
Hope this helps.
-Doctor Kathleen The Math Forum
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